By using the identity cos2A=1-2sin^2A show that cos4x = 1-8sin^2xcos^2x

Answer 1

cos 4x = 1 - 2sin^2 (2x)
= 1 - 2(sin 2x)(sin 2x)
= 1 - 2(2sinxcosx)(2sinxcosx)
= 1 - 8(sinxcosx)^2
or
= 1 - 8(sin^2 x)(cos^2 x) as required

Answer 2

thank you!